That's a good point, and I share that concern to some extent. But in thinking about it I guess I'm of the impression this happens anyway with private ISPs and the government? Private courts, state privilege, etc. Maybe if it were through the USPS it would force some transparency as well due to it not being private.
Also, I would be concerned if all the private ISPs disappeared also. Ideally I'd like to see something like is the case with physical delivery, where you have the USPS, FexEx, UPS, DHL, etc. Having the USPS be an ISP of sorts would hopefully not kill private offerings, along the same lines. Especially so given that we're in a de facto monopoly situation at the level of specific geographic locations often now. Introducing competition where the market has failed to do so shouldn't be a problem, and if it is, there are larger issues.
If anything I could see this being selling point for private ISPs, "use us and don't worry about the government because we have everything locked down in X, Y, and Z manner."